Help with output

This is a discussion on Help with output within the C Programming forums, part of the General Programming Boards category; Have the following Gauss Elim code from text: Not printing out correct code: SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS USING GAUSSIAN ...

  1. #1
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    May 2009
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    Help with output

    Have the following Gauss Elim code from text:

    Not printing out correct code:


    SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS
    USING GAUSSIAN ELIMINATION

    This program uses Gaussian Elimination to solve the
    system Ax = B, where A is the matrix of known
    coefficients, B is the vector of known constants
    and x is the column matrix of the unknowns.
    Number of equations: 3

    Enter elements of matrix [A]
    A(1,1) = 0
    A(1,2) = -6
    A(1,3) = 9
    A(2,1) = 7
    A(2,2) = 0
    A(2,3) = -5
    A(3,1) = 5
    A(3,2) = -8
    A(3,3) = 6

    Enter elements of [B] vector
    B(1) = -3
    B(2) = 3
    B(3) = -4

    SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS

    The solution is
    x(1) = 0.000000
    x(2) = -1.#IND00
    x(3) = -1.#IND00
    Determinant = -1.#IND00
    Press any key to continue . . .

    Should be 1.058824, 1.823529, 0.882353, det= -102.0000

    Any suggestions?- I tried to check- need fresh set of eyes

    Code:
    //Modified Code from C Numerical Methods Text
    
    #include <stdio.h>
    #include <math.h>
    #define MAXSIZE 20
    
    //function prototype
    int gauss (double a[][MAXSIZE], double b[], int n, double *det);
    
    int main(void)
    {
        double a[MAXSIZE][MAXSIZE], b[MAXSIZE], det;
        int i, j, n, retval;
        
    	printf("\n \t SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS");
    	printf("\n \t USING GAUSSIAN ELIMINATION \n");
    	printf("\n This program uses Gaussian Elimination to solve the");
    	printf("\n system Ax = B, where A is the matrix of known");
    	printf("\n coefficients, B is the vector of known constants");
    	printf("\n and x is the column matrix of the unknowns.");
    
    	//get number of equations
    	n = 0;
        while(n <= 0 || n > MAXSIZE)
    	{
    		printf("\n Number of equations: ");
    		scanf ("%d", &n);
    	}
    
    	//read matrix A
    	printf("\n Enter elements of matrix [A]\n");
    	for (i = 0; i < n; i++)
    		for (j = 0; j < n; j++)
    		{
    			printf(" A(%d,%d) = ", i + 1, j + 1);
    			scanf("%lf", &a[i][j]);
    		}
        //read {B} vector
        printf("\n Enter elements of [B] vector\n");
    	for (i = 0; i < n; i++)
    	{
    		printf(" B(%d) = ", i + 1);
    		scanf("%lf", &b[i]);
    	}
        
    	//call Gauss elimination function
    	retval = gauss(a, b, n, &det);
    
    	//print results
    	if (retval == 0)
    	{
    		printf("\n\t SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS\n");
    		printf("\n\t The solution is");
    		for (i = 0; i < n; i++)
    			printf("\n \t x(%d) = %lf", i + 1, b[i]);
    		printf("\n \t Determinant = %lf \n", det);
    	}
    	else
    		printf("\n \t SINGULAR MATRIX \n");
    
        return 0;
     }
    
    /* Solves the system of equations [A]{x} = {B} using       */
    /* the Gaussian elimination method with partial pivoting.  */
    /* Parameters:                                             */
    /*      n         - number of equations                    */
    /*      a[n][n]   - coefficient matrix                     */
    /*      b[n]      - right-hand side vector                 */
    /*      *det      - determinant of [A]                     */
    
    int gauss (double a[][MAXSIZE], double b[], int n, double *det)
    {
        double tol, temp, mult;
    	int npivot, i, j, l, k, flag;
    
    	//initialization
    	*det = 1.0;
    	tol = 1e-30;        //initial tolerance value
    	npivot = 0;
    
    	//forward elimination
    	for (k = 0; k < n; k++)
    	{
    		//search for max coefficient in pivot row- a[k][k] pivot element
    		for (i = k; i < n; i++)
    		{
    			if (fabs(a[i][k]) > fabs(a[k][k]))
    			{
    				//interchange row with maxium element with pivot row
    				npivot++;
    				for (l = 0; l < n; l++)
    				{
    				   temp = a[i][l];
    				   a[i][l] = a[k][l];
    				   a[k][l] = temp;
    				}
    				temp = b[i];
    				b[i] = b[k];
    				b[k] = temp;
    			}
    		}
    		//test for singularity
    		if (fabs(a[k][k]) < tol)
    		{
               //matrix is singular- terminate
    		   flag = 1;
    		   return flag;
    		}
            //compute determinant- the product of the pivot elements
    		*det = *det * a[k][k];
    
    		//eliminate the coefficients of X(I)
    		for (i = k; i < n; i++)
    		{
    			mult = a[i][k] / a[k][k];
    			b[i] = b[i] - b[k] * mult;  //compute constants
    			for (j = k; j < n; j++)     //compute coefficients
    				a[i][j] = a[i][j] - a[k][j] * mult;
    		}
    	}
    	//adjust the sign of the determinant
    	if(npivot % 2 == 1)
    	  *det = *det * (-1.0);
    
    	//backsubstitution
    	b[n] = b[n] / a[n][n];
    	for(i = n - 1; i > 1; i--)
    	{
    		for(j = n; j > i + 1; j--)
    			b[i] = b[i] - a[i][j] * b[j];
    		b[i] = b[i] / a[i - 1][i];
    	}
    	flag = 0;
    	return flag;
    }

  2. #2
    and the Hat of Guessing tabstop's Avatar
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    I'm thinking you should find the largest value in a given column first, then swap that with to the correct position -- as it is you're doing who knows how many swaps, which can affect the sign of your determinant. (I don't see how that fixes the problem, so there's bound to be something else as well.)

  3. #3
    and the Hat of Guessing tabstop's Avatar
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    Your eliminate coefficients loop starts one row too early -- you always wipe out the row you're trying to keep before starting, meaning that every other entry becomes x/0.

  4. #4
    Registered User
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    Code:
    //eliminate the coefficients of X(I)
    		for (i = k + 1; i < n; i++)
    		{
    			mult = a[i][k] / a[k][k];
    			b[i] = b[i] - b[k] * mult;  //compute constants
    			for (j = k; j < n; j++)     //compute coefficients
    				a[i][j] = a[i][j] - a[k][j] * mult;
    		}
    	}


    SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS
    USING GAUSSIAN ELIMINATION

    This program uses Gaussian Elimination to solve the
    system Ax = B, where A is the matrix of known
    coefficients, B is the vector of known constants
    and x is the column matrix of the unknowns.
    Number of equations: 3

    Enter elements of matrix [A]
    A(1,1) = 0
    A(1,2) = -6
    A(1,3) = 9
    A(2,1) = 7
    A(2,2) = 0
    A(2,3) = -5
    A(3,1) = 5
    A(3,2) = -8
    A(3,3) = 6

    Enter elements of [B] vector
    B(1) = -3
    B(2) = 3
    B(3) = -4

    SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS

    The solution is
    x(1) = 3.000000
    x(2) = -6.142857
    x(3) = 0.167910
    Determinant = -102.000000
    Press any key to continue . . .

    The determinate is correct now- but the solution does not match the one got be hand which is correct...what else needs to be changed elsewhere...I have tried...

  5. #5
    and the Hat of Guessing tabstop's Avatar
    Join Date
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    I suppose your backsubstitution starts in the wrong place as well. (There is no such thing as row n in a nxn matrix in C.)

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